So this is a project I wanted to engage in- To make a set of 10+ super-budget 60-card decks that are simple, relatively easy to play, relatively easy to understand, and bring across the fundamentals of how Magic Works. We've since gone way past 10, with tons more in the works, and I've really enjoyed the challenge of trying to make these decks easy to play and understand, fun, and all under a $15 budget, sideboard included.
The main goal here is that you could easily build these deck for a low cost and use them as an easy introduction to how magic works, to teach a group of new players both how to play, and give them a sense of Why, a sense of what fun things they're getting into. These decks aren't gonna be particularly good, or even legal in any particular format if it stops me from including a card I think is good for the deck, but they should be fun and interesting without being too hard to get into. They should be an easily-accessible example of how fun Magic: The Gathering can be.
This is one of the more advanced decks- Not really the first decks you want people learning with, but a sweet, budget deck you can use once new players are already on their feet to really knock their socks off and get them to think about something you can do in Magic that they might not have otherwise realized. Alt-win-conditions sort of automatically get you in that category, you know?
So one of the things I do to make these decks is that I just look at all the cards in a given 2-or-3 color combination, organized by cmc, to just give those multicolor cards the first chance to slot into these decks and ensure that new players get to feel like they got their hands on some sweet cards only their color-combo plays. As a result, I ran across Biovisionary quite a bit when planning these decks, and the answer when I saw him was always "Soon. Not in this deck, but Soon." I had to give it a shot, it's just a fun and silly combo that any real brewer has to try and make playable at one point or another.
As for budget: Maindeck cost is currently at a little less than ~$11.15 (according to the middle blue numbers on this very site under estimated value), sideboard at about ~$3.30. Took a little finagling, since Commander means that every clone, copy and tutor effect they ever print will always have demand for it, no matter how many they make, but we got there.
So mostly this section is going to be notes on why I think these are good cards to learn from:
Biovisionary is the obvious star here- you need to end your turn with 4+ Copies of this bad boy in play. They can be the real deal, they can be clones, they can be token, they could even be effects that only last until end of turn, though we don't have any of those here.
To Copy Biovisionary, we have Renegade Doppleganger, which can turn into a biovisionary when it Enters the battlefield, or into a Clone from Cackling Counterpart. Counterpart is 1 clone for 3 cmc, which is great, and a chance for an additional clone for 7 if the game goes really long without a victory.
To Find your Biovisionaries, the reliable way is to use Diabolic Tutor, but the more brute-force method is to peel through your deck with Forsee, trying to track down more clones and/or more tutors while you control the board.
To keep from dying, you have Agony Warp, Essence Scatter, Murder and Negate, all classics that need no introduction. Mizzium Skin and Ranger's Guile also serve to let you protect your board against removal, to keep the combo running, where Mizzium lets you overload it to protect your whole board (though not from most boardwipes), and Ranger's Guile can let you take a sweet block or two with your 2/3 visionaries against aggressive decks.
Manabase is meant to be a touch lacking, but also super-budget. Look, you try to build a 3-color mana base for less than $2, it's gonna suck, alright? That's the name of the game with budget 3-color manabases.
As for the sideboard, this IS supposed to be a sideboard they learn how to use, to make their deck perform better in the right matchups, or just in general to customize their decks within constraints.
Artisan of Forms increases your density of clones (and can be triggered by hexproof effects, or the -3/-0 half of Agony Warp, which I thought was particularly hilarious), while Wander in Death lets you retrieve some of your combo pieces after a boardwipe to start again.
Drown in Sorrow is a nice boardwipe of your own, murder and negate add to your answers, and Turn Aside works pretty well as another spell to defend your creatures with.